The vertical dynamic interaction between vehicle and railway track is simulated in the time domain using an extended state space vector approach. The track model includes a transition zone between slab track on a bridge and ballasted track on an embankment. By considering a multi-objective optimisation problem, solved using a genetic algorithm, selected vehicle and track responses are simultaneously minimised by optimising the distributions of rail pad stiffness and sleeper spacing in the transition zone. It is shown that the magnitudes of the maximum dynamic loads in the optimised transition zone can be reduced to be similar as the magnitudes far away from the transition zone.

2. Adaptive and semi-active vibration control of railway bridge dynamics

Andersson, Andreas

KTH, School of Architecture and the Built Environment (ABE), Civil and Architectural Engineering, Structural Engineering and Bridges.

Long Life Bridges is a Marie Curie 7th Framework Project funded under the Industry and Academia Partnerships and Pathways call, Grant Agreement No. 286276. The Project commenced in September 2011 and is continuing for 4 years until August 2015. The project vision is to extend the service lives of bridges through development of advanced assessment methods. The author wishes to acknowledge the financial contribution by the European Commission in supporting the project and funding this research.

The work presented in this report has been conducted at Roughan & O’Donovan Innovative Solutions, Dublin, Ireland, during the period of January to December 2012, under supervision of Associate Professor Alan O’Connor. The author has been seconded from the Royal Institute of Technology (KTH), Division of Structural Engineering and Bridges.

Within the project, experimental work to develop a prototype damper has been carried out at Trinity College Dublin (TCD), Department of Civil, Structural and Environmental Engineering. A special thank goes to Dr. Kevin Ryan and the laboratory staff at the Department for the help in manufacturing and testing the prototype damper.

Full-scale testing has been performed on a railway bridge in Sweden. The tests were funded directly by the Swedish Transport Administration (Trafikverket). The instrumentation and field measurements were performed by KTH in collaboration with the author.

The work presented, denoted secondment 1.1b, deals with development of adaptive and semi-active damping systems for railway bridges. The aim of the project is to develop methods for structural vibration control with applications for railway bridge dynamics. Much of the work has been related to a case study bridge.

There is constant demand on rail authorities to increase both the allowable axle loads and the allowable speed on existing railway lines. As an example, the Swedish Transport Administration has recently investigated the possibility of upgrading part of the main lines to allow for future high-speed trains. Some lines are also being investigated with the aim of allowing ore transports with higher axle loads and longer trains. A large portion of the bridge stock was designed for significantly lower axle loads and only very few have been designed to account for dynamic effects. Increased dynamic effects may result in exceedance of dynamic design criteria, reduced service life due to fatigue, or even failure. Through better quantification of risk, it is often possible to prove that speeds can be increased with no adverse effect. However, for bridges where the level of risk is too high, a cost-effective means of reducing dynamic effects on bridges are active and semi-active control system. Semi-active control is well established in other fields and could prove to be a beneficial technique to allow train speeds to be increased.

The concept of structural vibration control is to attenuate the dynamic response of a structure by means of an external damping device. Due to changes in either loading or structural behaviour, the properties of the damper device may need to be changed to efficiently mitigate vibrations. Two main principles of damper devices are commonly used; tuned mass dampers and shock absorbers. Tuned mass dampers consist of a suspended mass mounted on the main structure. Due to a phase-shift, the vibration of the suspended mass partly counteracts the corresponding motion of the main structure. Changing the stiffness of the suspended mass results in a variable adaptive tuned mass damper. Shock absorbers rely on producing the counteracting force by means of increased viscous damping. Devices with variable viscous damping are often categorised as semi-active. Fully active systems rely on producing the counteracting force by means of a load actuator. Adaptive and semi-active systems generally require much less energy to operate compared to fully active systems.

3. Capacity assessment of arch bridges with backfill

Andersson, Andreas

KTH, School of Architecture and the Built Environment (ABE), Civil and Architectural Engineering, Structural Design and Bridges.

The work presented in this thesis comprises the assessment of existing arch bridges with overlying backfill. The main objective is to estimate the load carrying capacity in ultimate limit state analysis. A case study of the old Årsta railway bridge is presented, serving as both the initiation and a direct application of the present research. The demand from the bridge owner is to extend the service life of the bridge by 50 years and increase the allowable axle load from 22.5 to 25 metric tonnes. The performed analyses show a great scatter in estimated load carrying capacity, depending on a large number of parameters. One of the factors of main impact is the backfill material, which may result a significant increase in load carrying capacity due to the interaction with the arch barrel. Based on theoretical analyses, extensive conditional assessments and the demand from the bridge owner, it was decided that the bridge needed to be strengthened.

The author, in close collaboration with both the bridge owner and the persons performing the conditional assessment, performed the development of a suitable strengthening. The analyses showed a pronounced three-dimensional behaviour, calling for a design using non-linear finite element methods. Due to demands on full operability during strengthening, a scheme was developed to attenuate any decrease in load carrying capacity. The strengthening was accepted by the bridge owner and is currently under construction. It is planned to be finalised in 2012.

The application of field measurements to determine the structural manner of action under serviceability loads are presented and have shown to be successful. Measured strain of the arch barrel due to passing train has been performed, both before, during and after strengthening. The results serve as input for model calibration and verification of the developed strengthening methods.

The interaction of the backfill was not readily verified on the studied bridge and the strengthening was based on the assumption that both the backfill and the spandrel walls contributed as dead weight only. The finite element models are benchmarked using available experimental results in the literature, comprising masonry arch bridges with backfill loaded until failure. Good agreement is generally found if accounting for full interaction with the backfill. Similarly, accounting for the backfill as dead weight only, often results in a decrease in load carrying capacity by a factor 2 to 3. Still, several factors show a high impact on the estimated load carrying capacity, of which many are difficult to accurately assess. This suggests a conservative approach, although partial interaction of the backfill may still increase the load carrying capacity significantly.

This report present results from simulations of simply supported concrete slab bridges for railway traffic. The geometry follows the Swedish standard deck models according to design drawing B2447-2 and B2447-8, with span lengths ranging from 2-8 m. For each bridge four different configurations are studied; straight or skewed bridge deck and short or long edge beams. In addition, a case of higher mass due to increased ballast depth is studied. In total 78 different bridge configurations are included.

According to the numerical models the first natural frequency range from about 15-80 Hz depending on span length and configuration. In all simulations the first three modes of vibration are included. The limit criteria is a peak deck acceleration of 3.5 m/s2 when loaded by the HSLM-A train model. Including a speed safety factor 1.2 according to EN 1991-2 results in an allowable speed that range from 175-350 km/h depending on the bridge configuration. The allowable speed is somewhat higher for the skewed bridges compared to straight bridges. Increased mass results in lower acceleration but also lower resonance speed. An increase in ballast depth from 0.6 to 1.2 m generally results in lower allowable speed, except for the shortestbridges in the study.

It should be noted that the above conclusions are based only on simulations. Before upgrading these bridges to speeds higher than 200 km/h experimental validation is recommended. On the other hand, most existing real trains are likely to result insignificantly lower dynamic response compared to the HSLM-A trains.

In this report, the load capacity of concrete slabs subjected to concentrated loads is studied, considering both the static load capacity and the response due to impact of a falling mass. The purpose of the study is to gain more knowledge on the static and dynamic behaviour of the slabs and to use that knowledge in the assessment of the load capacity of inner lining systems in tunnels. The methodology involves experimental testing of a series of slabs, validation of numerical models and simulating the response of the inner lining system.

A total of 18 slabs were manufactured, consisting of shotcrete and reinforcement mesh. Some of the slabs also included steel fibre reinforced concrete (SRFC). The size of the slabs were 1.75×1.75×0.12 m, suspended in four hangers #1.2 m and loaded centric on an area of 0.2×0.2 m. In addition, a series of core samples and beams were cut from two of the slabs for material testing and verification of numerical models.

From the static load tests of the slabs, the load at cracking was obtained at 50 – 60 kN with a vertical midpoint displacement of 0.6 – 1.0 mm. The ultimate load ranged from 60 – 80 kN. The slabs showed significant ductility with a peak displacement of about 70 – 80 mm at post-failure. All slabs showed a two-way flexural failure. The concrete cover was in average 30 mm, measured from the compressive side, resulting in little difference between the crack load and the ultimate load. A vertical displacement of about 1 – 2 mm was required to obtain a crack width of 0.2 mm. Three slabs with only SRFC were tested until static failure, the ultimate load ranged from 85 – 90 kN but with less ductility compared to the slabs with rebar mesh.

Impact load tests were performed using a steel mass of 600 kg. The free fall height was varied from 1 – 2 m. The peak impact load varied from 200 – 250 kN, without any clear correlation with the height. The corresponding impulse load varied from 4.0 – 5.5 kNs with a clear correlation to the height. All slabs subjected to impact load showed a one-way flexural failure, the residual strength after impact was sufficient to carry the static load of the steel weight. Several of the slabs showed significant fallout of concrete during impact, in one extreme case a total of 16 kg. Three slabs were tested with an outer layer of 30 mm of SRFC, none of these slabs showed any significant fallout.

The static and dynamic response of the slabs have been simulated using nonlinear FE-models. The models generally show good agreement, both for static load, crack widths and response during impact. Similar models were used to simulate the response of the inner lining system. The results indicate a significant load capacity, both due to static and impact loading. The models are however not able to account for potential punching failure.

In this paper, a load capacity assessment and strengthening measures of a multi-span railway arch bridge with backfill are presented. The bridge is located in Stockholm, Sweden, and constitute a vital link for the national railway network. The bridge consists of 20 concrete arches with overlying backfill, each with a span of 20 m. After more than 80 years of service, severe deterioration of the concrete was found during conditional assessments. A load capacity assessment was performed and the theoretical ultimate load was found to be highly dependent on the development of soil pressures along the arch barrel. The demands from the railway authority are to increase the allowable axle load from 22,5 to 25 tonnes and extend the service life by 50 years. Due to the uncertainties in structural behaviour and progressing degradation, extensive strengthening measures for the arch barrels were decided. To allow for full traffic at all times, the strengthening was performed in stages, to minimize any temporary reduction in load capacity due to removal of existing material. The strengthening was designed using non-linear finite element analysis and each stage of strengthening has been verified using in-situ field measurements.

In this report the analysis of 278 existing railway bridges is presented. The aim is to investigate how many of these bridges that potentially can be upgraded to higher speeds, with a target of 250 km/h. Due to the vast amount of bridges and the limited resources, the analyses are performed using simplified 2D models. The analysis is afflicted with several uncertainties, both regarding input parameters as well as model uncertainties. The results should therefore be interpreted carefully and primarily serve as an indicator for which bridges that may or may not meet the requirements. Large uncertainties are especially expected for portal frame bridges due to its inherently large interaction with the surrounding embankment and 3D behaviour.

The results from the analysis show that a total of 22 bridges theoretically fail to meet the dynamic requirements. A combination of refined analysis and experimental validation is recommended to better assess the dynamic response for these bridges. Among the most critical cases are several steel-concrete composite bridges, that due to a combination of low mass and low natural frequency may be prone to resonant loading. Retrofitting with external dampers may for some bridges be a viable solution.

The present thesis comprises a case study of the risk of fatigue of the railway bridges chaining between Stockholm Central Station and the district Söder Mälarstrand. A large number of fatigue-related cracks in the bridges at Söderström and Söder Mälarstrand have been known for a long time. During a capacity assessment of the current bridges, a large number of connections have been identified as critical concerning fatigue resistance. The route is the most frequent in all of Sweden and the simplified methods of fatigue assessment defined by Banverket may not always be applicable.

A conventional capacity assessment has shown numerous exceeds in fatigue resistance, using the stated safety margins. No fatigue cracks have been identified at the locations showing the largest theoretical risk of fatigue, in spite of extensive investigations. The conventional calculations are based on a uniform stress collective and a fixed number of stress cycles, independent of the actual traffic volume. According to the regulations stated by Banverket, the assessment may optionally be performed using historical data of the gross tonnage and standardised traffic loading. Such calculations have been undertaken and show even greater risk of fatigue, compared to the conventional assessment. To estimate the risk of fatigue in more detail, a method has been used, based on estimations of the real traffic volume and its distributions. The analysis is based on available data of the traffic volume and may be applied to other railway bridges on other locations.

Besides theoretical analyses, field measurements have been performed. In 2006, former Carl Bro AB carried out strain gauge measurements on the bridge passing Söder Mälarstrand and the viaduct south of Söder Mälarstrand. The measurements comprised a small amount of individual train passages. During 2008, the division of Structural Design and Bridges at KTH performed an extensive field measurement programme on the bridge passing Söderström. Continuous measurements collecting data of all traffic during a period of one month was performed.

The simulations are based on a 2D TTBI model with linear Hertzian contact that allows for loss of contact. The model has been verified against both other numerical simulations as well as experiments, all with good agreement. The parametric study consists of a large number of theoretical bridges, all optimized to reach the limit of either vertical deck acceleration or vertical deck displacement. The study comprises both single- and double track bridges.

The track irregularities are found to be of paramount importance. Two different levels are therefore studied; “higher track quality” corresponding to a well-maintained track for high-speed railways and “lower track quality” corresponding to the Alert Limit in EN 13848-5. The final conclusions are based on the “lower track quality” in order not to underestimate the risk of running safety and passenger comfort. Simulations with the bridge excluded show that the additional contribution from the bridge is low, especially for the lower track quality.

The existing limit for vertical deck acceleration is set to 5 m/s2 in EN 1990 A2 and is based on a very simple assumption of the gravity acceleration reduced by a factor 2. The results in this report show that this likely is a too conservative measure of the running safety. Based on the wheel–rail forces from the simulations, the resulting wheel unloading factor and duration of contact loss does not reach critical values before the deck acceleration is beyond 30 m/s2.

In EN 1990 A2, a vertical car body acceleration of 1 m/s2 is stipulated as “very good level of comfort” and is indirectly limited by the vertical deck displacement. Good agreement is generally found in the simulations between deck displacement and expected car body acceleration. In the simulations, the limit for car body acceleration is always exceeded before the running safety is compromised.

This report present result from dynamic analyses of railway bridges for high-speed trains. A comparison of the dynamic response in 2D vs. 3D has been performed for a limited selection of slab bridges, beam bridges and box girder bridges. Each cross-section has been optimized based on the dynamic requirements for dynamics in 2D, without any consideration of the static design. In many cases, the cross-section probably needs to be increased to fulfil the static load capacity.

Slab bridges with a span length from 10 – 25 m and 1 – 4 spans have been analysed. In several cases, mostly for shorter spans, the natural frequency for bending is lower in 3D compared to 2D. The reason is due to a smaller contributing width, owing to shear-lag. This results in a lower resonance speed and therefore often a larger dynamic response within the same speed range. Apart from that, the dynamic response is found to be similar in 3D compared to 2D. The influence of torsional does not appear to be governing the response for the studied cases.

Using the same method, beam bridges with span length from 20 – 40 m and 1 – 4 spans have been analysed. Similar to the slab bridges, the 3D-model of the beam bridges show lower natural frequency in bending compared to the 2D-model, owing to shear-lag. For double-track bridges, the difference in response between 2D and 3D-models are similar to the findings for the slab bridges. For single-track bridges, some cases of the 3D-model shows significantly lower response without pronounced resonance peaks in the same speed interval as the 2D-model. The reason is likely a combination of the support eccentricity and the mass of the bridge, which for vertical bending results in horizontal inertia. It is shown that this can be simulated with a modified 2D-model in most cases.

Box girder bridges with span length from 40 – 70 m in 1 – 3 spans have also been analysed. Due to the larger torsional stiffness, the torsional mode is often much higher than the first bending mode. Also, the shear-lag effect seems to be smaller and the response from the 3D-model agrees well with the corresponding 2D-model.

In the case dynamic assessment is performed using the simplified methods according to (Svedholm & Andersson, 2016), it is suggested that the following is considered:

Shear-lag and the eccentricity at the supports should be considered when estimating the first natural frequency for bending, n0, preferably using a 3D-model.

If the first torsional mode nT < 1.2n0, a full dynamic analysis in 3D should be performed.

In the case a 3D-model shows several closely spaced bending modes with similar shape, a full dynamic analysis in 3D should be performed.

KTH, School of Architecture and the Built Environment (ABE), Civil and Architectural Engineering, Structural Engineering and Bridges.

Karoumi, Raid

KTH, School of Architecture and the Built Environment (ABE), Civil and Architectural Engineering, Structural Engineering and Bridges. KTH, School of Engineering Sciences (SCI), Centres, The KTH Railway Group.

This paper presents some recent research on railway bridge dynamics with application to buried flexible structures. Based on a combination of simulations and full-scale testing, current research indicates that a rather comprehensive numerical model is required to accurately describe the response from passing trains.

In this paper, dynamic analyses and field measurements of a tied arch railway bridge is presented. Excessive vibrations of the hangers were obtained, caused by resonance during train passages. The resulting increase of the stress level and number of stress cycles were shown to decrease the fatigue service life significantly. The most critical section is a threaded turnbuckle connection of the hangers. Due to low damping of the hangers, more than 50 % of the cumulative fatigue damage was related to free vibrations after train passage. Passive dampers were installed to attenuate the vibrations by means of increased damping. A combination of field measurements and numerical models are used to investigate the behavior of the bridge and the impact of increased hanger damping.

The following paper discusses different aspects of railway bridge dynamics, comprising analysis, modelling procedures and experimental testing. The importance of realistic models is discussed, especially regarding boundary conditions, load distribution and soil-structure interaction. Two theoretical case studies are presented, involving both deterministic and probabilistic assessment of a large number of railway bridges using simplified and computationally efficient models. A total of four experimental case studies are also introduced, illustrating different aspects and phenomena in bridge dynamics. The excitation consists of both ambient vibrations, train induced vibrations, free vibrations after train passages and controlled forced excitation.

In this paper, a bi-directional multi-passive tuned mass damper is presented. The applicationfor the damper is on vertical hangers of an existing steel arch railway bridge.The hangers have been found susceptible to resonance and the resulting stressesresults in a reduced service life due to fatigue. Due to different boundaryconditions, the natural frequencies of the hangers are different in thelongitudinal and the transverse direction. In addition, the natural frequenciesincrease during train passage, due to increased tensile force in the hangers. Aprototype of the damper has been developed, consisting of two suspended massescoupled in series. Different lateral suspensions are used to obtain differentnatural frequencies in the longitudinal and the transverse direction. One massis tuned to the conditions of the fully loaded bridge and the other mass to theunloaded bridge. The performance of the damper is verified using controlledloading under laboratory conditions and the results are compared with a finiteelement model. The damper is shown to perform as expected and the motion of thetwo masses is near uncoupled. Finally, the performance of the damper isverified by in-situ testing on the case study bridge.

19. External damping of stay cables using adaptive and semi-active vibration control

Andersson, Andreas

et al.

KTH, School of Architecture and the Built Environment (ABE), Civil and Architectural Engineering, Structural Engineering and Bridges.

Karoumi, Raid

KTH, School of Architecture and the Built Environment (ABE), Civil and Architectural Engineering, Structural Engineering and Bridges.

In this paper, the performances of different external damping systems for stay cables are studied based on numerical simulations. Two types of dampers have been analysed; a near anchorage viscous damper and a tuned mass damper (TMD) mounted near the midspan of the stay cable. For the passive case, both dampers are tuned to the fundamental mode of vibration of the cable. The optimal viscous damping for the near anchorage damper is determined based on well-known equations for a taut string. For the TMD, parametrical studies have been performed to determine the optimal damping ratio as function of the damper mass. The resulting vibration mitigation from the two systems are also studied for higher modes of vibration and the potential increase in performance using an adaptive or semi-active vibration control system is studied.

In this paper, a semi-active control system for vibration mitigation of railway bridges is presented. The real time frequency response is estimated using a short-time Fourier transform, employing curve fitting to relevant peaks for increased accuracy. A control algorithm developed in Matlab® is linked to a commercial FE-software, facilitating application on arbitrary structures. A numerical study of an existing tied arch railway bridge is presented. From earlier field measurements and numerical analysis, resonance of several hangers during train passage was observed. This was shown to significantly reduce the fatigue service life of the hangers and for the most critical section about 50% of the cumulative damage was related to free vibrations. A system of passive dampers was later installed and the increase in resulting damping was measured. Within the present study, the previous results are reanalysed and compared with a semi-active approach. The natural frequencies of the hangers vary as a result of the variation in axial force. A semi-active control system has the potential to improve the vibration response of the structure when compared to the installed passive system.

In this paper, the advantage of an adaptive damping system is presented. A damper with variable stiffness is tuned based on estimates of the real-time frequency response, facilitating optimal vibration mitigation. The performance of the developed routines is investigated on an existing tied arch railway bridge. Based on previous field measurements, resonant behaviour of several hangers was found. In combination with low structural damping, the induced stresses resulted in a reduced fatigue service life. Passive dampers are currently installed on the longer hangers, each tuned to the fundamental natural frequency of the individual hanger. However, increased axial force during train passage results in a significant variation in natural frequency, with an apparent risk of detuning the passive dampers. The predicted performance of an adaptive damping system to account for this variation in dynamic behaviour is presented and its potential application is discussed.

In this paper, fatigue assessment of a steel railway bridge is presented. The bridge is located in central Stockholm, Sweden, and is one of the most vital links for the railway network. The bridge services both freight trains and commuter trains with more than 500 passages per day. The main load bearing structure is designed as a steel grillage of welded I-beams. Fatigue critical sections have been identified at locations where secondary bracing systems are welded to the flanges of the I-beams. Both numerical simulations and extensive field measurements have shown a significant exceedance of the theoretical fatigue service life. Based on analysis of local stress concentrations, improvement of fatigue critical details have been suggested. The decrease in stress concentration is demonstrated both by numerical simulations and in-situ field measurements and shows a significant improvement when estimating the remaining fatigue service life.

This paper presents a full-scale dynamic testing on a simply supported railway bridge with integrated end-shields, by using a hydraulic exciter. Experimental frequency response functions are determined based on load controlled frequency sweeps. Apart from accurate estimates of natural frequencies, damping and mode shapes, the experimental testing also gives valuable information about the dynamic characteristics at resonance and amplitude dependent nonlinearities. Numerical models are used to simulate the dynamic response from passing trains which is compared to experimental testing of similar train passages. The results show that the bridge deck is partially constrained due to the interaction between the end-shields and the wing walls with the surrounding soil. Measurements at the supports also show that the flexibility of the foundation needs to be accounted for. An updated numerical model is able to accurately predict the response from passing trains. The response is lower than that predicted from the initial simulations and the bridge will fulfil the design requirements regarding vertical deck acceleration.

The aim of this thesis is to analyse the effects of train induced vibrations in a steel Langer beam bridge. A case study of a bridge over the river Ljungan in Ånge has been made by analysing measurements and comparing the results with a finite element model in ABAQUS. The critical details of the bridge are the hangers that are connected to the arches and the main beams. A stabilising system has been made in order to reduce the vibrations which would lead to increased life length of the bridge.

Initially, the background to this thesis and a description of the studied bridge are presented. An introduction of the theories that has been applied is given and a description of the modelling procedure in ABAQUS is presented.

The performed measurements investigated the induced strain and accelerations in the hangers. The natural frequency, the corresponding damping coefficients and the displacement these vibrations leads to has been evaluated. The vibration-induced stresses, which could lead to fatigue, have been evaluated. The measurement was made after the existing stabilising system has been dismantled and this results in that the risk of fatigue is excessive. The results were separated into two parts: train passage and free vibrations. This shows that the free vibrations contribute more and longer life expectancy could be achieved by introducing dampers, to reduce the amplitude of the amplitude of free vibrations.

The finite element modelling is divided into four categories: general static analysis, eigenvalue analysis, dynamic analysis and detailed analysis of the turn buckle in the hangers. The deflection of the bridge and the initial stresses due to gravity load were evaluated in the static analysis. The eigenfrequencies were extracted in an eigenvalue analysis, both concerning eigenfrequencies in the hangers as well as global modes of the bridge. The main part of the finite element modelling involves the dynamic simulation of the train passing the bridge. The model shows that the longer hangers vibrate excessively during the train passage because of resonance. An analysis of a model with a stabilising system shows that the vibrations are damped in the direction along the bridge but are instead increased in the perpendicular direction. The results from the model agree with the measured data when dealing with stresses. When comparing the results concerning the displacement of the hangers, accurate filtering must be applied to obtain similar results.

n this article, the use of external damping systems for vibration mitigation of railway bridge dynamics is studied. For a presented case study bridge, the performance of different tuned mass damper systems (TMDs) is studied. During train passage, the change in dynamic characteristics of the bridge may produce a significant detune to a passive TMD. Therefore, routines for a variable stiffness TMD using incremental frequency estimates are developed. Based on numerical simulations, the cumulative fatigue damage is calculated for different damper systems. Due to resonant behavior, the results are found to highly depend on the train speed. Based on an assumed probability density function for the train speed, fragility curves are produced to express the probability of fatigue failure as a function of the number of train passages.

The inner lining concept is a method to prevent water leakage and the risk of icing inside tunnels and is frequently used in countries with cold climate. Blocks of falling ice may result is a severe safety risk in both road and railway tunnels. Although several established inner lining systems exist, finding the optimal solution considering function, maintenance- and investment cost is a challenging task. A new system has recently been used in Sweden and is due to its success planned to be used for the Stockholm Bypass, an 18 km road tunnel project in Stockholm.

A set of design criterions has been stipulated for the inner lining system. In this paper, the case of impact loading from falling rocks is studied. The inner lining system is required to withstand the impact of a 600 kg block landing on a square surface of 0.2x0.2 m. The free fall height, i.e. the distance to the rock surface, is typically less than 0.5 m but may span up to 1.5 m in some cases. A too conservative design may result in an unnecessary thick structure and lack of knowledge of the impact phenomena may result in an unsafe design.

An extensive experimental program has been performed, consisting of representative parts of the inner lining system. A mass of 600 kg is dropped onto the structure and the results are compared with numerical simulations. The experiments show that the current system is rather ductile but that local concrete fallouts may occur at extreme free fall heights.

Inner lining system in tunnels is a method to prevent water ingress and forming of ice in the traffic area. A solution that is common in Norway is based on stretching a sealing membrane between rock anchorages that forms a gap to the primary rock strengthening. The membrane is in turn protected by a layer of shotcrete towards the traffic area. The rock strengthening is designed to resist all loads from the rock mass independent of the inner lining system. A problem is however how to perform inspections and conditional assessment of the rock strengthening, since the gap is usually small. Other topics are what loads the inner lining system should be designed for. In TRVK Tunnel 11, the load of a local falling rock of 600 kg is stipulated, assuming to act on a surface of 0.2×0.2 m. Furthermore, the inner lining system should be designed to resist what is connoted as an extreme rock load of 6 metric ton, acting on a 1×1 m area, even when a primary rock strengthening is present. Similar inner lining systems have been used in e.g. Norra länken, parts of Citybanan in Stockholm and is planned to be used for the Stockholm Bypass project.

In the present paper, results from a recent research project are presented, aiming at investigating the structural manner of action of the aforementioned inner lining system. A series of concrete slabs have been tested, both until static failure and with a 600 kg drop weight from different heights. All tested slabs resulted in flexural failure and showed a significant ductility. For several of the slabs tested for impact loading, significant spalling from the soffit was obtained, at the most corresponding to a mass of 16 kg. Three of the slabs tested for impact load were manufactured with an outer layer of steel fibre reinforced shotcrete. None of these slabs showed any significant spalling, despite a free fall height up to 2 m.

Several FE-analyses have also been performed, accounting for the nonlinear material properties of concrete. The results showed good agreement with the conducted experiments, both regarding static loading, cracking and impact load. A similar analysis was also done for the whole inner lining system. The results showed a larger load capacity compared to the experiments, but still with a rather localised failure.

This paper deals with the assessment of cable forces in existing cable supported bridges using the ambient vibration method. A case study of the Älvsborg suspension bridge in Sweden is presented. Dynamic measurements of the backstays and hangers as well as on each strand in one of the splay chambers have been carried out. The measured frequencies are evaluated and calculations of corresponding axial force in the cable structures are performed taking into account the cable sag, boundary conditions and flexural rigidity. Modal analyses have been used to study the shape of vibration and for comparison with finite element models.

In this paper, results from full-scale tests on a corrugated soil-steel flexible culvert for railway traffic are presented. The bridge was instrumented with strain gauges, accelerometers and displacement gauges, measuring the response from passing trains. The aim of the measurement campaign was to gain knowledge of the dynamic behaviour due to train induced vibrations, both of the bridge structure and the overlying railway embankment. From the measured data, the load distribution and soil-stiffness can be estimated. The results also serve as input for calibration of numerical models that are used for predicting the behaviour due to high-speed trains.

This paper describes the development of a hydraulic bridge exciter and its first pilot testing on a full scale railway bridge in service. The exciter is based on a hydraulic load cylinder with a capacity of 50 kN and is intended for controlled dynamic loading up to at least 50 Hz. The load is applied from underneath the bridge, enabling testing while the railway line is in service. The system is shown to produce constant load amplitude even at resonance. The exciter is used to experimentally determine frequency response functions at all sensor locations, which serve as valuable input for model updating and verification. An FE-model of the case study bridge has been developed that is in good agreement with the experimental results.

KTH, School of Architecture and the Built Environment (ABE), Civil and Architectural Engineering, Structural Engineering and Bridges.

Andersson, Andreas

KTH, School of Architecture and the Built Environment (ABE), Civil and Architectural Engineering, Structural Engineering and Bridges.

Karoumi, Raid

KTH, School of Architecture and the Built Environment (ABE), Civil and Architectural Engineering, Structural Engineering and Bridges. KTH, School of Engineering Sciences (SCI), Centres, The KTH Railway Group.

The train running safety on non-ballasted bridges is studied based on safety indices from the vertical wheel–rail forces. A 2D train–track–bridge interaction model that allows for wheel–rail contact loss is adopted for a comprehensive parametric study on high-speed passenger trains. The relation between bridge response and vehicle response is studied for more than 200 theoretical bridges in 1–3 spans. The bridge's inuence on running safety and passenger comfort is differentiated from the influence of the track irregularities. The Eurocode bridge deck acceleration limit for non-ballasted bridges is 5 m/s2 based on the assumed derailment risk at 1g from wheel–rail contact loss. This study shows that the running safety indices are not compromised for bridge accelerations up to 30 m/s2. Thus, accelerations at 1g do not in itself lead to contact loss and there is potential to enhance the Eurocode safety limits for non-ballasted bridges.

34. Train running safety on non-ballasted bridges

Arvidsson, Therese

et al.

KTH, School of Architecture and the Built Environment (ABE), Civil and Architectural Engineering, Structural Engineering and Bridges.

Andersson, Andreas

KTH, School of Architecture and the Built Environment (ABE), Civil and Architectural Engineering, Structural Engineering and Bridges. Swedish Transport Adm Trafikverket, Solna, Sweden..

Karoumi, Raid

KTH, School of Architecture and the Built Environment (ABE), Civil and Architectural Engineering, Structural Engineering and Bridges.

The train running safety on non-ballasted bridges is studied based on safety indices from the vertical wheel-rail forces. A 2D train- track-bridge interaction model that allows for wheel-rail contact loss is adopted for a comprehensive parametric study on high-speed passenger trains. The relation between bridge response and vehicle response is studied for more than 200 theoretical bridges in 1-3 spans. The bridge's influence on running safety and passenger comfort is differentiated from the influence of the track irregularities. The Eurocode bridge deck acceleration limit for non-ballasted bridges is 5 m/s(2) based on the assumed derailment risk at 1 g from wheel-rail contact loss. This study shows that the running safety indices are not compromised for bridge accelerations up to 30 m/s(2). Thus, accelerations at 1 g do not in itself lead to contact loss and there is potential to enhance the Eurocode safety limits for non-ballasted bridges.

The railway track, being discretely supported at each sleeper, has a varying stiffness. The periodic loading from the wheels passing the sleepers at a certain speed introduces the sleeper passing frequency. This excitation of the track is a well-known source of vibration for track embankments. However, the interaction between the sleeper passing frequency and the railway bridge vibration is not well studied. In this paper, a 2D finite element model is calibrated against measured frequency response functions from a short span portal frame bridge. The track is modelled with the rail as a beam resting on discrete spring–dashpots at each sleeper location. In replicating the measured signals from train passages, the train load is typically idealized as moving forces. For the case study bridge, the resulting bridge deck acceleration amplitudes from such a moving force analysis were significantly lower compared to the measured signal. It is shown that if the wheel mass is introduced in the model, and thus the sleeper passing frequency, the model provides results in good agreement with measured data. Thus, it is demonstrated that the bridge deck vibration can be greatly amplified if the sleeper passing frequency matches a bridge frequency. A sensitivity analysis shows that the effect of the sleeper passing frequency is sensitive to track stiffness and bridge frequency.

36. Influence of the ballasted track on the dynamic properties of a truss railway bridge

Bornet, Lucie

et al.

KTH, School of Architecture and the Built Environment (ABE), Civil and Architectural Engineering, Structural Engineering and Bridges.

Andersson, Andreas

KTH, School of Architecture and the Built Environment (ABE), Civil and Architectural Engineering, Structural Engineering and Bridges.

Zwolski, Jaroslaw

Battini, Jean-Marc

KTH, School of Architecture and the Built Environment (ABE), Civil and Architectural Engineering, Structural Engineering and Bridges.

This article presents numerical and experimental analyses of a steel truss railway bridge. The main interest of this work is that dynamic experiments have been performed before and after the ballasted track was placed on the bridge. Consequently, it has been possible to quantify the effect of the ballast and the rails on the dynamic properties of the bridge. For that, two finite element models, with and without the ballasted track, have been implemented and calibrated using the experimental results. It appears that the ballast gives an additional stiffness of about 25-30% for the lowest three eigenmodes. This additional stiffness can be only partly explained by the stiffness of the ballast. In fact, it seems that this additional stiffness is also due to a change of the support conditions.

The following report comprises extensive dynamic analyses of railway bridges, with the aim of presenting an initial estimate on the feasibility to allow future high-speed trains on existing bridges. The lines studied are the West main line between Stockholm and Gothenburg, the South main line between Stockholm and Malmö and the West coast line between Gothenburg and Malmö. This comprises more than 1000 bridges.

Detailed studied of all bridges is beyond the scope of the present study. Instead, a combination of detailed studies and probability-based methods has been chosen. The analyses have been limited to beam- and slab bridges and portal frame bridges, constituting about 90 % of the total included bridge stock. The requirements for the dynamic analyses follow Eurocode EN-1990 and EN-1991-2 and are mainly related to the vertical acceleration of the bridge deck, limited to 3.5 m/s2. The aim of the study is to investigate allowable speeds up to250 km/h.

Based on extensive parametric analyses, a number of factors have been identified as decisive for the dynamic bridge behaviour. Many of these parameters are difficult to properly estimate and often influence the structural response in a non-regular manner. Extensive Monte-Carlo simulations have been performed based on simplified 2D-models. The results show that about 70 % of the beam- and slab bridges and about 50 % of the portal frame bridges are expected to exceed the design criterions stated by the Eurocode. Even if the allowable speed would be decreased to150 km/h, 15 % of the beam- and slab bridges and 30 % of the portal frame bridges are expected to exceed the criterions. Expected probabilities for each bridge are presented in Appendix F, to be used for further investment cost estimates.

The presented results are a consequence of the strict criterions stated by the Eurocode, also valid for design of new bridges. Other conditions regarding e.g. train load model or frequency range for evaluation of accelerations will be critical for the results. One of the main remaining questions is the dynamic behaviour of short span bridges appertaining high natural frequencies. The dynamic response from such bridges often constitutes of transient loading rather than resonance. According to the previous Swedish bridge design code BV-Bro, the frequency range was limited to 30 Hz. In Eurocode the frequency range is limited to the third mode of vibration for each studied structural member. This often results in significantly higher frequency ranges, especially for short span bridges. The validity of these criterions must be investigated further.

The Swedish government is considering upgrading the train speed along three railway lines in the Southern part of Sweden from 200 km/h to 250 km/h. According to the current design code, this requires that the bridges be examined with dynamic simulations to avoid excessive vibrations. This paper employs a method that can be used at an early stage to estimate the expected cost of upgrading a bridge network. The results revealed that 70% of the plate/beam bridges, 64% of the closed slab-frame bridges, and 41% of the open slab-frame bridges are expected to not fulfill the requirement on the maximum bridge deck acceleration for ballasted tracks.

The Swedish government is considering upgrading the train speed along three railway lines in the Southern part of Sweden from 200 km/h to 250 km/h. According to the current design code, this requires that the bridges be examined with dynamic simulations to avoid excessive vibrations. This paper employs a method that can be used at an early stage to estimate the expected cost of upgrading a bridge network. The results revealed that 70% of the plate/beam bridges, 64% of the closed slab-frame bridges, and 41% of the open slab-frame bridges are expected to not fulfil the requirement on the maximum bridge deck acceleration for ballasted tracks.

43. Load testing of the new Svinesund Bridge

Karoumi, Raid

et al.

KTH, School of Architecture and the Built Environment (ABE), Civil and Architectural Engineering, Structural Design and Bridges.

Andersson, Andreas

KTH, School of Architecture and the Built Environment (ABE), Civil and Architectural Engineering, Structural Design and Bridges.

The New Svinesund Bridge at the border between Sweden and Norway has recently been opened to traffic. Due to the uniqueness of design and the importance of the bridge, an extensive long-term monitoring program was inititated. This paper briefly describes the instrumentation of the bridge and focuses on the comprehensive static and dynamic load tests that were performed just before bridge opening. Some interesting results are presented and compared with those predicted by theory.

During annual inspections of one of Sweden's most important railway bridges, the Soderstrom Bridge in central Stockholm, cracks in the web of the main steel beams have been discovered. Extensive theoretical work has been undertaken to assess the remaining service life of the bridge. Furthermore, the bridge has recently been instrumented to enhance the theoretical predictions by monitoring the real railway traffic as well as the response of the bridge. This article describes the monitoring program and the analysis methods used. Some interesting results regarding the remaining fatigue life are presented.

During routine inspections of the Soderstrom Bridge in central Stockholm, one of Sweden's most important railway bridges, cracks were found in the web of the main steel beams. The finding initiated theoretical Studies which showed that the cracks developed mainly due to poorly designed connections of the cross beams and out-of-plane bending of the web. The Studies also showed an alarming result regarding the remaining fatigue life of the stringers and the cross beams. However, no cracks or other damage have been found on these components during the inspections. To explore the differences between the theoretical indications and the inspected reality, an extensive monitoring program has been performed. This article describes the monitoring program and the analysis methods used. Some results regarding the remaining fatigue life based on measured and theoretical values are presented. (C) 2009 Elsevier Ltd. All rights reserved.

This report contains a parametric study on the dynamic response of railway bridges on flexible supports. The results are based on simulations using 2D and 3D models. The dynamic stiffness of the supports is described by separate models of the foundation, including relevant stress and strain dependent soil properties from permanent loading that is linearized in a subsequent dynamic analysis. The complex-valued dynamic stiffness constitutes the boundary conditions in a separate analysis of the bridge superstructure that is solved in frequency domain.

Two different foundation types are studied; shallow slab foundation with relatively good ground conditions, and pile group foundations with relatively poor ground conditions. In both cases, the foundation slab and the pile group have fixed geometry. In the parametric study, the corresponding vertical static foundation stiffness range from 2 – 20 GN/m for the slab foundation and 5 – 25 GN/m for the pile group foundation.

For the slab foundations, both the stiffness and damping highly depends on the properties of the soil, foundation depth and geometry of the foundation slab. For the pile group foundations, the stiffness is mainly governed by the pile group and the damping by the soil.

Based on the simulations, the additional damping from the slab foundation is in most cases negligible. Only for relatively soft foundations and short-span bridges significant additional damping is seen. For the pile group foundations, the additional damping is in some cases significant, especially for deeper foundations and short-span bridges. Considering a lower bound of the parametric study does however result in a negligible contribution.

The dynamic response from passing trains show that the assumption of fixed supports in most cases is conservative. However, the flexible supports may result in a lower natural frequency that should be accounted for in order to not underestimate the resonance speed of the train.

If flexible supports are included in a dynamic analysis, both the stiffness and damping component needs to be included. The frequency-domain approach presented in this report is a viable solution technique but is not implemented in most commercial software used in the industry.

This paper deals with the dynamic effects on a tied arch railway bridge during train passages. The bridge is located in Ange municipality in central Sweden. Large vibrations of the hangers were observed during train passages and field measurements have been performed to study the train induced vibrations of the hangers. According to the Palmgren-Miners linear damage rule, there is a great risk of fatigue in the threaded parts of the hangers. The low damping in the hangers has a large influence of the risk of fatigue failure. A 3D finite element model of the bridge has been developed where the dynamic vehicle-bridge interaction was modelled using contact surface formulation with a sprung mass train system. The measured data results are compared with the results from the FE model to give a better understanding of the dynamic behaviour of the bridge.